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find much of interest in this unique work and many confirma-
tions of the views at which Poincare had arrived independently
before he saw the results of the questionnaire. A few points of
general interest may be noted before we quote from Poincare.
The early interest in mathematics of those who were to be-
corae great mathematicians has been frequently exemplified in
preceding chapters. To the question *At what period ... and
under what circumstances did mathematics seize you?' ninety-
three replies to the first part were received: thirty-five said
before the age of ten; forty-three said eleven to fifteen; eleven
said sixteen to eighteen; three said nineteen to twenty; and the
lone laggard said twenty-six.
Again, anyone with mathematical friends will have noticed
that some of them like to work early in the morning (I know one
very distinguished mathematician who begins his day's work
at the inhuman hour of five a.m.), while others do nothing till
after dark. The replies on this point indicated a curious trend -
possibly significant, although there are numerous exceptions:
mathematicians of the northern races prefer to work at night,
while the Latins favour the morning. Among night-workers
prolonged concentration often brings on insomnia as they grow
older and they change - reluctantly - to the morning. Felix
Klein, who worked day and night as a young man, once indi-
cated a possible way out of this difficulty. One of his American
students complained that he could not sleep for thinking of his
mathematics. *Can't sleep, eh?' Klein snorted. 'What's chloral
for?' However, this remedy is not to be recommended indiscri-
minately; it probably had something to do with Klein's OTTO
tragic breakdown.
Probably the most significant of the replies were those
received on the topic of inspiration versus drudgery as the
source of mathematical discoveries. The conclusion is that
'Mathematical discoveries, small or great ... are never bom of
spontaneous generation. They always presuppose a soil seeded
with preliminary knowledge and well prepared by labour, botii
conscious and subconscious.*
Those who, like Thomas Alva Edison, have declared thai
genius is 99 per cent perspiration and only 1 per cent inspira-